A Mathematical Framework for Understanding Recognition Systems

Abstract

AbstractRecognition plays a crucial role in the formation of social bonds, mate selection, kin selection and survival across species. However, a unifying framework for understanding recognition systems in biology is lacking. We, therefore, propose a theoretical framework for biological recognition utilizing basic principles from category theory, information theory, dynamical systems modeling and optimization theory. We define the two types of recognition, individual recognition (IR) and class-level recognition (CR), asfunctorsbetween categories ofstimuliandresponses. IR producesuniqueresponses for each individual, while CR producessharedresponses for multiple individuals of the same class. We identify five conditions –universality, low entropy, unfalsifiability, uniform convergenceandcognitive limit– that must hold for robust IR systems, which we term “signature systems.” Further, we model signature systems asattractor stateswith perspectives from both statistical information processing and dynamical systems. Our framework provides a basis for advancing understanding of the mechanisms underlying biological recognition and its implications for communication and behavior. Overall, the mathematical conceptualization of IR provides a basis for advancing our understanding of communication and the evolution of language.